Kagome Topology in Two-Dimensional Noble-Metal Monolayers

TL;DR

Problem: establishing the viability of elemental 2D kagome lattices in Cu, Ag, and Au under dynamic and thermal conditions. Approach: perform first-principles DFT (PBE, PAW) with SOC, DFPT phonons, and AIMD to study mechanical, dynamical, and thermal stability, including a 5% biaxial strain test and Born criteria check. Key findings: unstrained kagome phases are dynamically unstable; 5% strain stabilizes Ag and Au; Cu remains unstable; at finite temperature Cu reconstructs to trigonal, Ag collapses at 300 K, and Au shows a kagome–trigonal near-degeneracy. Significance: demonstrates strain- and size-driven stabilization pathways for 2D kagome metals and informs substrate-supported synthesis, highlighting the role of relativistic Au bonding.

Abstract

Two-dimensional (2D) metallic lattices with kagome topology provide a unique platform for exploring the interplay between geometric frustration, reduced coordination, and lattice stability in elemental systems. Motivated by the recent experimental realization of atomically thin gold layers and kagome goldene, we present a first-principles investigation of free-standing kagome monolayers of Cu, Ag, and Au. Using density functional theory combined with lattice dynamics and ab initio molecular dynamics, we systematically assess their structural, mechanical, dynamical, and thermal stability. All kagome monolayers satisfy the 2D Born criteria and exhibit relatively low in-plane stiffness compared to graphene and hexagonal goldene, reflecting the porous nature of the kagome lattice and its metallic bonding. Among the three systems, the Au-based lattice displays the highest in-plane Young's modulus. Phonon calculations reveal that the unstrained kagome phase is dynamically unstable for all metals. However, a moderate biaxial tensile strain of 5% stabilizes the Ag and Au monolayers, while Cu retains residual unstable modes. Finite-temperature simulations further show that Cu rapidly reconstructs toward a trigonal lattice, Ag remains metastable at low temperature but collapses at room temperature, and Au exhibits competing kagome and trigonal motifs at 300 K, indicating near-degeneracy between these phases. These results establish that strain engineering and atomic size are key determinants of the stability of metallic kagome monolayers and provide guidance for future substrate-supported realizations.

Figures (3)

• Figure 1: Optimized atomic structures of free-standing kagome monolayers composed of (a) Cu, (b) Ag, and (c) Au. Dashed hexagons indicate the primitive unit cell containing three atoms. The kagome topology is formed by corner-sharing triangular units, resulting in a coordination number of four. All structures are shown after full in-plane relaxation, with a fixed vacuum spacing along the out-of-plane direction.
• Figure 2: Phonon dispersion relations of free-standing kagome monolayers composed of (a) Cu, (b) Ag, and (c) Au along the high-symmetry path $\Gamma$--M--K--$\Gamma$. Gray curves correspond to the unstrained lattices, while black curves show the phonon spectra under 5% biaxial tensile strain.
• Figure 3: AIMD results for free-standing metallic kagome monolayers. Time evolution of the total energy per atom at 50 K (blue curves) and 300 K (red curves) for (a) Cu, (b) Ag, and (c) Au.